On the ‐action on G‐semistable locally free sheaves on

We show that the divisor of jumping lines of any , the moduli space of Gieseker‐semistable locally free sheaves of rank 2 on with , is reduced for . By a lemma of Artamkin this implies, that there are exactly ‐orbits in , the subset of those , which are trivial at a certain line .     

Universal Plane Curve and Moduli Spaces of 1-dimensional Coherent Sheaves

We show that the universal plane curve M of fixed degree d ≥ 3 can be seen as a closed subvariety in a certain Simpson moduli space of 1-dimensional sheaves on ?₂ contained in the stable locus. The universal singular locus of M coincides with the subvariety M′ of M consisting of sheaves that are not locally free on their support. It turns out that the blow up Bl _M′ M may be naturally seen as a compactification of M _B  = M?M′ by vector bundles (on support).     

L-fuzzy集理论的范畴基础与层表示

鉴于L-fuzzy集在理论上的重要性和应用上的广泛性,旨在建立L-fuzzy集理论的范畴基础与它的层表示,提出完备范畴中对象上的格值结构概念,这一概念是L-fuzzy结构在范畴层面上的提升,进一步提出完备范畴上格值结构提升范畴概念,证明了在集合范畴中L-fuzzy结构与格值结构是同构的.以集层、群层、环层和左R-模层以及Grothendieck层等概念为基础,提出完备范畴中对象上的层结构以及完备范畴上层结构提升范畴概念,证明了在集合范畴中L-fuzzy结构与层结构也是同构的.     

截尾样本下,具有共同尺度参数的多总体指数分布的参数估计

讨论了在截尾样本下,具有共同尺度参数的多总体指数分布的参数估计问题,证明了尺度参数及位置参数的最佳仿射同变估计是不容许的,且给出了相应的改进估计.     

On contractible

We present a very short proof of a well-known result, that for each there exists a contractible -dimensional compactum, non-embeddable into .

     

A class of minimax estimators of a normal quantile

The estimation problem of the quantiles of a normal distribution with both parameters unknown, is considered. We construct a class of minimax procedures each of which improves upon the traditional (best equivariant) estimator of a quantile different from the median. For this purpose a differential inequality and a family of its solutions is found.     

Equivariant K-Homology and Restriction to Finite Cyclic Subgroups

For a discrete group G, we prove that a G-map between proper G–CW-complexes induces an isomorphism in G-equivariant K-homology if it induces an isomorphism in C-equivariant K-homology for every finite cyclic subgroup C of G. As an application, we show that the source of the Baum–Connes assembly map, namely K _* ^G (E(G, in)), is isomorphic to K _* ^G (E(G, )), where E(G, ) denotes the classifying space for the family of finite cyclic subgroups of G. Letting be the family of virtually cyclic subgroups of G, we also establish that and related results.     

Mackey Formula in Type A

The statement (and the proof) of Theorem 4.1.1 of the paper‘Mackey formula in type A’ [Proc. London. Math.Soc. (3) 80 (2000) 545–574] is false. In this corrigendumwe provide a correct statement (and a correct proof). As a consequence,we see that Corollary 4.1.2 of the paper holds. So all the otherstatements in the paper are correct (up to minor misprints...).2000 Mathematical Subject Classification: 20G05, 20G40.     

Cycles and Spectra

Some recent work on spaces of algebraic cycles is surveyed. The main focus is on spaces of real and quaternionic cycles and their relation to equivariant Eilenberg- MacLane spaces.Dedicated to IMPA on the occasion of its 50^th anniversary     

Equivariant Cyclic Cohomology of H-Algebras

We define an equivariant K ₀-theory for Yetter–Drinfeld algebras over a Hopf algebra with an invertible antipode. We then show that this definition can be generalized to all Hopf-module algebras. We show that there exists a pairing, generalizing Connes pairing, between this theory and a suitably defined Hopf algebra equivariant cyclic cohomology theory.